generally known as the nebular hypothesis--that the heavenly bodies
were formed by the slow contraction of heated nebulous masses, is
indicated by so many facts that it seems scarcely possible to doubt it
except on the theory that the laws of nature were, at some former time,
different from those which we now see in operation. Granting the
evolutionary hypothesis, every star has its lifetime. We can even lay
down the law by which it passes from infancy to old age. All stars do
not have the same length of life; the rule is that the larger the star,
or the greater the mass of matter which composes it, the longer will it
endure. Up to the present time, science can do nothing more than point
out these indications of a beginning, and their inevitable consequence,
that there is to be an end to the light and heat of every heavenly
body. But no cautious thinker can treat such a subject with the ease of
ordinary demonstration. The investigator may even be excused if he
stands dumb with awe before the creation of his own intellect. Our
accurate records of the operations of nature extend through only two or
three centuries, and do not reach a satisfactory standard until within
a single century. The experience of the individual is limited to a few
years, and beyond this period he must depend upon the records of his
ancestors. All his knowledge of the laws of nature is derived from this
very limited experience. How can he essay to describe what may have
been going on hundreds of millions of years in the past? Can he dare to
say that nature was the same then as now?
It is a fundamental principle of the theory of evolution, as developed
by its greatest recent expounder, that matter itself is eternal, and
that all the changes which have taken place in the universe, so far as
made up of matter, are in the nature of transformations of this eternal
substance. But we doubt whether any physical philosopher of the present
day would be satisfied to accept any demonstration of the eternity of
matter. All he would admit is that, so far as his observation goes, no
change in the quantity of matter can be produced by the action of any
known cause. It seems to be equally uncreatable and indestructible. But
he would, at the same time, admit that his experience no more sufficed
to settle the question than the observation of an animal for a single
day would settle the question of the duration of its life, or prove
that it had neither beginning nor end. He would probably admit that
even matter itself may be a product of evolution. The astronomer finds
it difficult to conceive that the great nebulous masses which he sees
in the celestial spaces--millions of times larger than the whole solar
system, yet so tenuous that they offer not the slightest obstruction to
the passage of a ray of light through their whole length--situated in
what seems to be a region of eternal cold, below anything that we can
produce on the earth's surface, yet radiating light, and with it heat,
like an incandescent body--can be made up of the same kind of substance
that we have around us on the earth's surface. Who knows but that the
radiant property that Becquerel has found in certain forms of matter
may be a residuum of some original form of energy which is inherent in
great cosmical masses, and has fed our sun during all the ages required
by the geologist for the structure of the earth's crusts? It may be
that in this phenomenon we have the key to the great riddle of the
universe, with which profounder secrets of matter than any we have
penetrated will be opened to the eyes of our successors.
IV
THE EXTENT OF THE UNIVERSE
We cannot expect that the wisest men of our remotest posterity, who can
base their conclusions upon thousands of years of accurate observation,
will reach a decision on this subject without some measure of reserve.
Such being the case, it might appear the dictate of wisdom to leave its
consideration to some future age, when it may be taken up with better
means of information than we now possess. But the question is one which
will refuse to be postponed so long as the propensity to think of the
possibilities of creation is characteristic of our race. The issue is
not whether we shall ignore the question altogether, like Eve in the
presence of Raphael; but whether in studying it we shall confine our
speculations within the limits set by sound scientific reasoning.
Essaying to do this, I invite the reader's attention to what science
may suggest, admitting in advance that the sphere of exact knowledge is
small compared with the possibilities of creation, and that outside
this sphere we can state only more or less probable conclusions.
The reader who desires to approach this subject in the most receptive
spirit should begin his study by betaking himself on a clear, moonless
evening, when he has no earthly concern to disturb the serenity of his
thoughts, to some point where he can lie on his back on bench or roof,
and scan the whole vault of heaven at one view. He can do this with the
greatest pleasure and profit in late summer or autumn--winter would do
equally well were it possible for the mind to rise so far above bodily
conditions that the question of temperature should not enter. The
thinking man who does this under circumstances most favorable for calm
thought will form a new conception of the wonder of the universe. If
summer or autumn be chosen, the stupendous arch of the Milky Way will
pass near the zenith, and the constellation Lyra, led by its beautiful
blue Vega of the first magnitude, may be not very far from that point.
South of it will be seen the constellation Aquila, marked by the bright
Altair, between two smaller but conspicuous stars. The bright Arcturus
will be somewhere in the west, and, if the observation is not made too
early in the season, Aldebaran will be seen somewhere in the east. When
attention is concentrated on the scene the thousands of stars on each
side of the Milky Way will fill the mind with the consciousness of a
stupendous and all-embracing frame, beside which all human affairs sink
into insignificance. A new idea will be formed of such a well-known
fact of astronomy as the motion of the solar system in space, by
reflecting that, during all human history, the sun, carrying the earth
with it, has been flying towards a region in or just south of the
constellation Lyra, with a speed beyond all that art can produce on
earth, without producing any change apparent to ordinary vision in the
aspect of the constellation. Not only Lyra and Aquila, but every one of
the thousand stars which form the framework of the sky, were seen by
our earliest ancestors just as we see them now. Bodily rest may be
obtained at any time by ceasing from our labors, and weary systems may
find nerve rest at any summer resort; but I know of no way in which
complete rest can be obtained for the weary soul--in which the mind can
be so entirely relieved of the burden of all human anxiety--as by the
contemplation of the spectacle presented by the starry heavens under
the conditions just described. As we make a feeble attempt to learn
what science can tell us about the structure of this starry frame, I
hope the reader will allow me to at least fancy him contemplating it in
this way.
The first question which may suggest itself to the inquiring reader is:
How is it possible by any methods of observation yet known to the
astronomer to learn anything about the universe as a whole? We may
commence by answering this question in a somewhat comprehensive way. It
is possible only because the universe, vast though it is, shows certain
characteristics of a unified and bounded whole. It is not a chaos, it
is not even a collection of things, each of which came into existence
in its own separate way. If it were, there would be nothing in common
between two widely separate regions of the universe. But, as a matter
of fact, science shows unity in the whole structure, and diversity only
in details. The Milky Way itself will be seen by the most ordinary
observer to form a single structure. This structure is, in some sort,
the foundation on which the universe is built. It is a girdle which
seems to span the whole of creation, so far as our telescopes have yet
enabled us to determine what creation is; and yet it has elements of
similarity in all its parts. What has yet more significance, it is in
some respects unlike those parts of the universe which lie without it,
and even unlike those which lie in that central region within it where
our system is now situated. The minute stars, individually far beyond
the limit of visibility to the naked eye, which form its cloudlike
agglomerations, are found to be mostly bluer in color, from one extreme
to the other, than the general average of the stars which make up the
rest of the universe.
In the preceding essay on the structure of the universe, we have
pointed out several features of the universe showing the unity of the
whole. We shall now bring together these and other features with a view
of showing their relation to the question of the extent of the universe.
The Milky Way being in a certain sense the foundation on which the
whole system is constructed, we have first to notice the symmetry of
the whole. This is seen in the fact that a certain resemblance is found
in any two opposite regions of the sky, no matter where we choose them.
If we take them in the Milky Way, the stars are more numerous than
elsewhere; if we take opposite regions in or near the Milky Way, we
shall find more stars in both of them than elsewhere; if we take them
in the region anywhere around the poles of the Milky Way, we shall find
fewer stars, but they will be equally numerous in each of the two
regions. We infer from this that whatever cause determined the number
of the stars in space was of the same nature in every two antipodal
regions of the heavens.
Another unity marked with yet more precision is seen in the chemical
elements of which stars are composed. We know that the sun is composed
of the same elements which we find on the earth and into which we
resolve compounds in our laboratories. These same elements are found in
the most distant stars. It is true that some of these bodies seem to
contain elements which we do not find on earth. But as these unknown
elements are scattered from one extreme of the universe to the other,
they only serve still further to enforce the unity which runs through
the whole. The nebulae are composed, in part at least, of forms of
matter dissimilar to any with which we are acquainted. But, different
though they may be, they are alike in their general character
throughout the whole field we are considering. Even in such a feature
as the proper motions of the stars, the same unity is seen. The reader
doubtless knows that each of these objects is flying through space on
its own course with a speed comparable with that of the earth around
the sun. These speeds range from the smallest limit up to more than one
hundred miles a second. Such diversity might seem to detract from the
unity of the whole; but when we seek to learn something definite by
taking their average, we find this average to be, so far as can yet be
determined, much the same in opposite regions of the universe. Quite
recently it has become probable that a certain class of very bright
stars known as Orion stars--because there are many of them in the most
brilliant of our constellations--which are scattered along the whole
course of the Milky Way, have one and all, in the general average,
slower motions than other stars. Here again we have a definable
characteristic extending through the universe. In drawing attention to
these points of similarity throughout the whole universe, it must not
be supposed that we base our conclusions directly upon them. The point
they bring out is that the universe is in the nature of an organized
system; and it is upon the fact of its being such a system that we are
able, by other facts, to reach conclusions as to its structure, extent,
and other characteristics.
One of the great problems connected with the universe is that of its
possible extent. How far away are the stars? One of the unities which
we have described leads at once to the conclusion that the stars must
be at very different distances from us; probably the more distant ones
are a thousand times as far as the nearest; possibly even farther than
this. This conclusion may, in the first place, be based on the fact
that the stars seem to be scattered equally throughout those regions of
the universe which are not connected with the Milky Way. To illustrate
the principle, suppose a farmer to sow a wheat-field of entirely
unknown extent with ten bushels of wheat. We visit the field and wish
to have some idea of its acreage. We may do this if we know how many
grains of wheat there are in the ten bushels. Then we examine a space
two or three feet square in any part of the field and count the number
of grains in that space. If the wheat is equally scattered over the
whole field, we find its extent by the simple rule that the size of the
field bears the same proportion to the size of the space in which the
count was made that the whole number of grains in the ten bushels sown
bears to the number of grains counted. If we find ten grains in a
square foot, we know that the number of square feet in the whole field
is one-tenth that of the number of grains sown. So it is with the
universe of stars. If the latter are sown equally through space, the
extent of the space occupied must be proportional to the number of
stars which it contains.
But this consideration does not tell us anything about the actual
distance of the stars or how thickly they may be scattered. To do this
we must be able to determine the distance of a certain number of stars,
just as we suppose the farmer to count the grains in a certain small
extent of his wheat-field. There is only one way in which we can make a
definite measure of the distance of any one star. As the earth swings
through its vast annual circuit round the sun, the direction of the
stars must appear to be a little different when seen from one extremity
of the circuit than when seen from the other. This difference is called
the parallax of the stars; and the problem of measuring it is one of
the most delicate and difficult in the whole field of practical
astronomy.
The nineteenth century was well on its way before the instruments of
the astronomer were brought to such perfection as to admit of the
measurement. From the time of Copernicus to that of Bessel many
attempts had been made to measure the parallax of the stars, and more
than once had some eager astronomer thought himself successful. But
subsequent investigation always showed that he had been mistaken, and
that what he thought was the effect of parallax was due to some other
cause, perhaps the imperfections of his instrument, perhaps the effect
of heat and cold upon it or upon the atmosphere through which he was
obliged to observe the star, or upon the going of his clock. Thus
things went on until 1837, when Bessel announced that measures with a
heliometer--the most refined instrument that has ever been used in
measurement--showed that a certain star in the constellation Cygnus had
a parallax of one-third of a second. It may be interesting to give an
idea of this quantity. Suppose one's self in a house on top of a
mountain looking out of a window one foot square, at a house on another
mountain one hundred miles away. One is allowed to look at that distant
house through one edge of the pane of glass and then through the
opposite edge; and he has to determine the change in the direction of
the distant house produced by this change of one foot in his own
position. From this he is to estimate how far off the other mountain
is. To do this, one would have to measure just about the amount of
parallax that Bessel found in his star. And yet this star is among the
few nearest to our system. The nearest star of all, Alpha Centauri,
visible only in latitudes south of our middle ones, is perhaps half as
far as Bessel's star, while Sirius and one or two others are nearly at
the same distance. About 100 stars, all told, have had their parallax
measured with a greater or less degree of probability. The work is
going on from year to year, each successive astronomer who takes it up
being able, as a general rule, to avail himself of better instruments
or to use a better method. But, after all, the distances of even some
of the 100 stars carefully measured must still remain quite doubtful.
Let us now return to the idea of dividing the space in which the
universe is situated into concentric spheres drawn at various distances
around our system as a centre. Here we shall take as our standard a
distance 400,000 times that of the sun from the earth. Regarding this
as a unit, we imagine ourselves to measure out in any direction a
distance twice as great as this--then another equal distance, making
one three times as great, and so indefinitely. We then have successive
spheres of which we take the nearer one as the unit. The total space
filled by the second sphere will be 8 times the unit; that of the third
space 27 times, and so on, as the cube of each distance. Since each
sphere includes all those within it, the volume of space between each
two spheres will be proportional to the difference of these
numbers--that is, to 1, 7, 19, etc. Comparing these volumes with the
number of stars probably within them, the general result up to the
present time is that the number of stars in any of these spheres will
be about equal to the units of volume which they comprise, when we take
for this unit the smallest and innermost of the spheres, having a
radius 400,000 times the sun's distance. We are thus enabled to form
some general idea of how thickly the stars are sown through space. We
cannot claim any numerical exactness for this idea, but in the absence
of better methods it does afford us some basis for reasoning.
Now we can carry on our computation as we supposed the farmer to
measure the extent of his wheat-field. Let us suppose that there are
125,000,000 stars in the heavens. This is an exceedingly rough
estimate, but let us make the supposition for the time being. Accepting
the view that they are nearly equally scattered throughout space, it
will follow that they must be contained within a volume equal to
125,000,000 times the sphere we have taken as our unit. We find the
distance of the surface of this sphere by extracting the cube root of
this number, which gives us 500. We may, therefore, say, as the result
of a very rough estimate, that the number of stars we have supposed
would be contained within a distance found by multiplying 400,000 times
the distance of the sun by 500; that is, that they are contained within
a region whose boundary is 200,000,000 times the distance of the sun.
This is a distance through which light would travel in about 3300 years.
It is not impossible that the number of stars is much greater than that
we have supposed. Let us grant that there are eight times as many, or
1,000,000,000. Then we should have to extend the boundary of our
universe twice as far, carrying it to a distance which light would
require 6600 years to travel.
There is another method of estimating the thickness with which stars
are sown through space, and hence the extent of the universe, the
result of which will be of interest. It is based on the proper motion
of the stars. One of the greatest triumphs of astronomy of our time has
been the measurement of the actual speed at which many of the stars are
moving to or from us in space. These measures are made with the
spectroscope. Unfortunately, they can be best made only on the brighter
stars--becoming very difficult in the case of stars not plainly visible
to the naked eye. Still the motions of several hundreds have been
measured and the number is constantly increasing.
A general result of all these measures and of other estimates may be
summed up by saying that there is a certain average speed with which
the individual stars move in space; and that this average is about
twenty miles per second. We are also able to form an estimate as to
what proportion of the stars move with each rate of speed from the
lowest up to a limit which is probably as high as 150 miles per second.
Knowing these proportions we have, by observation of the proper motions
of the stars, another method of estimating how thickly they are
scattered in space; in other words, what is the volume of space which,
on the average, contains a single star. This method gives a thickness
of the stars greater by about twenty-five per cent, than that derived
from the measures of parallax. That is to say, a sphere like the second
we have proposed, having a radius 800,000 times the distance of the
sun, and therefore a diameter 1,600,000 times this distance, would,
judging by the proper motions, have ten or twelve stars contained
within it, while the measures of parallax only show eight stars within
the sphere of this diameter having the sun as its centre. The
probabilities are in favor of the result giving the greater thickness
of the stars. But, after all, the discrepancy does not change the
general conclusion as to the limits of the visible universe. If we
cannot estimate its extent with the same certainty that we can
determine the size of the earth, we can still form a general idea of it.
The estimates we have made are based on the supposition that the stars
are equally scattered in space. We have good reason to believe that
this is true of all the stars except those of the Milky Way. But, after
all, the latter probably includes half the whole number of stars
visible with a telescope, and the question may arise whether our
results are seriously wrong from this cause. This question can best be
solved by yet another method of estimating the average distance of
certain classes of stars.